Question: Determine the value of the following complex number power. Your answer will be plotted in orange. $ ({ e^{\pi i / 4}}) ^ {12} $
Since $(a ^ b) ^ c = a ^ {b \cdot c}$ $ ({ e^{\pi i / 4}}) ^ {12} = e ^ {12 \cdot (\pi i / 4)} $ The angle of the result is $12 \cdot \frac{1}{4}\pi$ , which is $3\pi$ Our result is $ e^{\pi i}$.